are needed before solutions of large-scale chemically reacting, viscous flowfields can be considered routine enough to be used An implicit algorithm for computing viscous flows in chemical nonequilibrium is presented. Emphasis is placed on the numerical in other than a research environment.
efficiency of the time integration scheme, both in terms of per-This article represents the beginning of a research effort iteration workload and overall convergence rate. In this context, designed to focus on ways to improve the numerical efficiency several techniques are introduced, including a stable, ᏻ(m 2 ) approxiof algorithms for computing chemically reacting, viscous flow.
mate factorization of the chemical source Jacobian and implementa-
The paper is outlined as follows. In Section 2, the governing tions of V-cycle and filtered multigrid acceleration methods. A five species-seventeen reaction air model is used to calculate hyper-equations are briefly outlined and the discretization approach sonic viscous flow over a cylinder at conditions corresponding to is described. The basic implicit time integration scheme, a flight at 5 km/s, 60 km altitude and at 11.36 km/s, 76.42 km altitude. point Gauss-Seidel approach, is presented in Section 3. Several Inviscid calculations using an eleven-species reaction mechanism methods for the implicit treatment of the chemical source term including ionization are presented for a case involving 11.37 km/s are outlined in Section 4, including a new ᏻ(m 2 ) approximate flow at an altitude of 84.6 km. Comparisons among various options for the implicit treatment of the chemical source terms and among factorization approach (m is the number of chemical species).
different multilevel approaches for convergence acceleration are Section 5 describes the implementation of two multigrid presented for all simulations.